When you first acquire the tank on Assault on the Control Room, and clear out the Type-26 Wraith, the best way to take out the Banshee is to turn the tank around, look right up to the structure where it takes off from, and backup until you receive the checkpoint. Once the Banshee takes off, start moving forward and do not open fire until the Banshee has fired its Fuel Rod Cannon; after the round hits the ground, take aim and take it down.
Later on, after you move into the valley with the second set of Hunters, as soon as you get to the bottom of the slope, quickly turn around and head back up the ice ramp to take out the Covenant dropship attempting to flank you from behind. Be sure to watch out for your Marines, as they will also follow you up the slope.
Stay in the tank on "Delta Halo" when you proceed into the structures especially on legendary difficulty due to there being an abundance of Ghosts that are present within the structure. Despite the confined space the tank can be manuevered with relative ease through the structure. If playing co-op have the second player use the Warthog to protect the tank from the rear and to scout ahead.
In Halo: Combat Evolved, even small pieces of cover, such as the spires on the top of Blood Gulch's bases, can stop players taking damage. Taking cover behind these spires while the cannon fires and firing while it reloads is effective, just watch out for the machine gun, which at close range, is quite lethal.
In Halo: Combat Evolved where the driver is exposed, it is possible to eliminate him with a single shot from a sniper rifle. However, if the player fails to kill the driver and is exposed, his tactic may turn against him and result in his death. Because of that, this tactic can be suicidal in some occasions. The pistol can also be used this way, but it requires more shots than a sniper rifle.
Although you cannot ride on the tread covers like you could in Halo: Combat Evolved, a player who has taken the enemy's flag can still ride the tank by jumping on the tread cover and staying put; they will not fall off as usual and can ride all the way back to the base with extra firepower supporting you.